Báo cáo toán học: "On multicolor Ramsey number of paths versus cycles" pdf

... a corollary of more general results about the asymptotic results of the Ra msey number for three long even cycles. Recently, determination of some exact values of Ramsey numbers of type R( P i , ... three-color Ramsey numbers for paths versus a cycle, see [3, 4, 5, 13]. In this paper, we provide the exact value of the Ramsey numbers R(P n 1 , P n 2 , . . . , P n t , C...

Ngày tải lên: 08/08/2014, 12:23

... n , ensuring the validity of (6) is certainly weaker than the condition p  log n/ √ n.Wehave thus proved: Lemma 3 The expected number (X r ) of dominating sets of size r of the random graph G(n, ... p) 2r−s  n−2r+s the electronic journal of combinatorics 8 (2001), #R37 7 On the Domination Number of a Random Graph Ben Wieland Department of Mathematics University of Chicag...

Ngày tải lên: 07/08/2014, 06:22

... curve. Definition 2 The crossing number cr G of a graph G is the smallest crossing number of any drawing of G in the plane, where the crossing number cr D of a drawing D is the number of non-adjacent edges ... the same way as in the proof of Lemma 1. Lemma 3 Let λ be the number of distinct pairs of elements of B having the same cyclic ordering of edges incident on...

Ngày tải lên: 07/08/2014, 07:21

... 2. y u <y v . Repeating the proof of Case 1 with roles of A and B switched yields this case. The proof of Claim 3.2 is the same (with C in place of B). ProofofClaim3.3.Let A ∗ =2A, B ∗ = A ∗ − ... Theorem 2. ProofofTheorem2. Let A be a member of a set M = {M i } of translates of a centrally symmetric convex set in the plane such that the clique number of the intersection...

Ngày tải lên: 07/08/2014, 08:20

... coloring of a k-graph is a coloring of its vertices such that no edge is monochromatic, and the chromatic number is the minimum number of colors in a proper coloring. An easy consequence of the ... V be the vertex set of H. As usual, we write χ(H) for the chromatic number of H. Let ε > 0 be a sufficiently small fixed number. Throughout the paper, we will omit the use of...

Ngày tải lên: 07/08/2014, 21:20

... calculating some 3-color Ramsey numbers, Technical Report of Gda´nsk University of Technology, ETI Faculty 18/03 (2003). [8] Dzido T.: Multicolor Ramsey numbers for paths and cycles, Discuss. ... +2. the electronic journal of combinatorics 13 (2006), #R55 7 On some Ramsey and Tur´an-type numbers for paths and cycles Tomasz Dzido Institute of Mathematics, University of Gd...

Ngày tải lên: 07/08/2014, 13:21

... problem of computing the difference between the metric dimension and the determining number of graphs. We provide new proofs and results on the determining number of trees and Cartesian pr oducts of ... determining number of the wheel graphs is always 2 independently of the number of vertices. On the other hand, Shanmukha and Soor yanarayana [24] show that β(W 1,n−1 ) in-...

Ngày tải lên: 08/08/2014, 12:22

... J. Beck, On size Ramsey number of paths, trees and cycles I, J. Graph Theory 7 (1983), 115–130. [3] J. Beck, On size Ramsey number of paths, trees and cycles II. Mathematics of Ramsey Theory (Springer), ... Ramsey number) . When ρ(G) is the chromatic number χ(G), Burr, Erd˝os, and Lov´asz [5] showed that R χ (G) equals the Ramsey number of the family of homomorp...

Ngày tải lên: 08/08/2014, 14:23

... ∈ V (G), the number of edges of color 2 and 3 incident to v is at most 8 in each color, and their total number is at most 8 · 22 = 1 76. Since T (22, C 4 ) = 52 [8], the number of colored edges ... Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey 1, revision #12, August 2009, http://www.combinatorics.org. [6] Radziszowski S.P., Shao Z., Xu X.: Bounds o...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 09:46